Talk by David Field from Cornell University.  Given to the Redwood Center for Theoretical Neuroscience at UC Berkeley and also to the 2017 course in mining and modeling neuroscience data (course described at crcns.org).

Abstract
I will discuss some implications of an approach that attempts to describe the various non-linearities of neurons in the visual pathway using a geometric framework. This approach will be used to make a distinction between selectivity and hyper-selectivity. Selectivity will be defined in terms of the optimal stimulus of a neuron, while hyper-selectivity will be defined in terms of the falloff in response as one moves away from the optimal stimulus. With this distinction, I show that it is possible for a neuron to be very narrowly tuned (hyper-selective) to a broadband stimulus. We show that hyper-selectivity allows V1 neurons to break the Gabor-Heisenberg localization limit. The general approach will be used to contrast different theories of non-linear processing including sparse coding, gain control, and linear non-linear (LNL) models. Finally, I will show that the approach provides insights into the non-linearities found with overcomplete sparse codes ­ and argues that sparse coding provides the most parsimonious account of the common non-linearities found in the early visual system.

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